Elsevier

Physical Communication

Volume 34, June 2019, Pages 220-226
Physical Communication

Full length article
The probability of error in FSO communication system using Differential Chaos Shift Keying

https://doi.org/10.1016/j.phycom.2019.03.014Get rights and content

Abstract

In present-day communication system, Free Space Optical (FSO) communication is in demand due to its various advantages such as large bandwidth, high capacity, license-free spectrum, high directivity, low power consumption, cost effectiveness, etc. The basic concern for any communication system is its privacy and security. Although FSO communication is more secure as compared to conventional radio frequency (RF) systems, there are still chances of leakage of information. Here, chaotic signals are used in order to ensure the guaranteed reception only by the intended-receiver and not by any other external agent. In this manuscript, Differential Chaos Shift Keying (DCSK) in FSO system taking Gamma–Gamma turbulence model is studied as it is easy to implement and one of the robust techniques for wireless multipath channels. The system performance is analyzed using probability of error as a metric for various link lengths, spreading factor and turbulence condition. It is observed that an increase in spreading factor results in increase of average signal-to-noise ratio (SNR) for same link length, probability of error and turbulence conditions. Therefore we have to compromise between high SNR and security for DCSK based FSO communication system.

Introduction

Free Space Optical (FSO) communication system has proved to be a promising approach for high data rates, cost-effective, license-free, line-of-sight communication in recent years. In comparison to radio frequency (RF) counterpart, FSO communication system provides various reputable properties such as higher bandwidth, narrow beam divergence, low power and lesser mass requirements, security and high directivity [1]. The most admirable feature of any modern communication system is the amount of security and privacy provided by it. The nature of optical beams in FSO communication systems are highly directional in nature and so it is relatively difficult to intercept them. For this reason, FSO systems are considered more secure than RF systems and has applications in military, banking, etc. [2] where security and uninterrupted reception is critically important.

Though FSO seems to be very secure, there are many cases where the chances of leakage of information to some external agent or eavesdropper are viable. For instance, some part of optical beam may get scattered by the particles present in the atmosphere and then that part might be detected by an external agent who is not in line-of-sight (LOS) of both communication peers. Further, FSO communication can suffer from security in the cases when the main lobe of laser beam is wider than the field-of-view of the receiver. This typically happens for long distance communication e.g., ground-to-satellite FSO communication. Also, an intruder may interrupt the laser beam directly during line-of-sight communication. This is the case in which the transmitter and receiver will instantly get to know about the interruption and the communication can be suspended temporarily for security reasons. Moreover, there are cases in which the interruption is invisible and the transmitter and receiver will not have any knowledge of the eavesdropper collecting large amount of information. Fig. 1 depicts these invisible cases: (a) intruder can gather the spillage behind the receiver without the knowledge of receiver (b) intruder can interrupt near the transmitter.

In the last few years, FSO security has been studied a lot for the above mentioned reasons [3], [4]. Adding security to FSO systems by different types of methods have been studied by many investigators. One of the notable techniques that can be used for robust, flexible and secure transmission is by use of chaos signals with FSO systems [5], [6]. A signal is chaotic signal when it possesses these three properties — aperiodic, deterministic and depends on initial conditions of the system. Most of the research in the area of chaos signals with optical signals is mostly carried out in optical fiber environment [7], [8], so there is more scope in exploring chaos signals in FSO environment.

Chaos theory was first given by Lorenz in 1963 [9]. In 1990, the synchronous nature of chaotic signals was studied by Pecora and Carroll [10] and the possibility of synchronizing and controlling of chaos gave ideas for the proposal of various practical applications of chaos. The authors in [11], proved the synchronization property of chaos and gave the necessary and sufficient conditions for synchronization. Cuomo and Oppenheim [12] in 1993 were successful in constructing first ever Lorenz circuit and experimentally presented the first chaotic communication system. Since then, chaos has been playing a crucial role in communication. Further, chaotic communication makes use of chaotic signals as carrier unlike conventional communication system that uses sinusoidal carriers. This property of chaotic communication gives various advantages such as they are difficult to intercept, easily hidden from external prohibited receiver, immune to distortion and resistant to jamming [13].

Recently, chaos-based communication has been explored by various researchers. The signal is recovered at the receiver side by the essential property of chaotic signals i.e., self-synchronization property. The authors in [14] implemented this self-synchronized chaotic system in FSO and studied this system with different values of turbulence. An optical data beam is secured by chaos with acousto-optic cell-based free space optical link in [15]. In [16], secure optical link is established by the use of two synchronized lasers and chaotic signals in FSO link and also transmission of data is ensured and proved numerically. By using special reconfigurable tent map [17], security of FSO system is analyzed in [18]. Practical hardware implementation of proposed chaotic FSO system is carried out in [19] with the help of Field-Programmable Gate Array (FPGA) technology.

Chaos-based communication is categorized into coherent and non-coherent chaotic communication on the basis of detection process used. A proper synchronized chaos signal is needed at the receiver side in order to recover signal accurately in coherent detection methods. But in non-coherent detection, no proper synchronization is required, as data is recovered by detecting the features of received signal without generating any local chaotic signal at receiver end. Non-coherent schemes are similar to spread spectrum transmission or steganographic communication. Block diagram of steganographic system is shown in Fig. 2. Here the key/ spread spectrum code is embedded in the message before transmission. At the receiver end, the message is received using the same key. Therefore the possession of ’KEY ONLY’ will help in revealing the message. Thus the security level is lower as compared to the coherent schemes which require perfect carrier phase synchronization at the receiver. Coherent system gives better performance in additive white gaussian noise (AWGN) channels than non-coherent counterparts, however practically robust chaos synchronization techniques are yet not available for required signal-to-noise (SNR) conditions. Also, there is major requirement of reproduction of replica of chaos signals at the receiver side for reception of transmitted signal and that too remains a major technical limitation for practical implementation of coherent chaotic systems. In spite of less favorable performance, non-coherent systems are used because they do not require synchronization between transmitter and receiver. This method of detection is less complex, very robust to multipath channel and easy to implement as compared to coherent detection [20], [21].

Applications of coherent modulation schemes in FSO communication systems are discussed in [15], [16] [22]. Due to above mentioned disadvantages, limitations in practical implementation of chaotic synchronization in wireless context, applications of coherent modulation schemes in FSO communications are not much explored.

Differential Chaos Shift Keying (DCSK) is the basic non-coherent digital modulation scheme. As the research is growing in this area, many researchers have proposed variants of DCSK, such as, correlation delay shift keying (CDSK) [23], generalized extension of CDSK (GCDSK) [24], improved DCSK (I-DCSK) [25], short reference DCSK (SR-DCSK) [26], noise reduction DCSK (NR-DCSK) [27], etc. In DCSK system, each bit duration is split in two equal slots. First slot consists of chaotic signal taken as reference and other slot consists of reference signal or its inverted version depending upon the bit being transmitted. The main disadvantage of DCSK system is that the reference signal is sent in each time slot and this leads to high energy consumption, data rates are reduced and wideband delay lines are used. CDSK is the scheme in which the reference chaotic signal and the information bearing chaotic signal are added together instead of sequential transmission as done in DCSK. The transmitted signal is not repeated here so this scheme overcomes the drawbacks of DCSK. GCDSK is generalized extended version of CDSK, where a number of modulated delayed chaotic signals are taken and finally original chaotic signal is added with these delayed signals. This obtained signal is ready for transmission. Advantage of this scheme is that it allows simultaneous transmission of more than one information bearing signal and more than one reference signal. Let M chips per bit were used in DCSK for both reference and information bearing signal. In NR-DCSK, M/P samples are used. These samples are then duplicated P times. This scheme was proposed in order to reduce the noise content that existed in the received signal. SR-DCSK is short reference DCSK system that was introduced to reduce the delay line. This scheme reduces the complexity, increases data rates and energy efficiency as compared to conventional DCSK. I-DCSK is improved version of DCSK in which both reference and information bearing signals are transmitted in same time slot. Spectral efficiency of these systems are almost doubled as compared to conventional DCSK. Table 1 shows comparison between different types of digital non-coherent modulation schemes. These variants were proposed to improve the performance of DCSK, so, this modulation scheme is taken as a reference.

In this manuscript, the performance of non-coherent modulation technique is analyzed for FSO system. Gamma–Gamma turbulence model has been used for analysis. Section 2 presents system and channel model and further in Section 3 analytical expressions for probability of error Pe has been derived in terms of Meijer-G function for our proposed system. Finally, numerical results followed by conclusion are presented in Section 4 and Section 5, respectively.

Section snippets

System and channel model

DCSK is the simplest digital non-coherent modulation scheme [28]. Our proposed system including DCSK in FSO channel is shown with the help of block diagram in Fig. 3.

Chaos generator generates the signal xi. bj is the binary information that is to be transmitted in form of +1/1. si is the transmitted signal that is represented as [29] si=xi,1<iMbjxiM,M+1<i2M2M is the spreading factor. The transmitted signal in DCSK consists of two equal time slots for every one bit duration. The first slot

Calculation of probability of error

Error rate for DCSK in terms of instantaneous SNR per bit is given as in  [29], Pe(γb)=Qγb2(1+M2γb)1

As Q(x)=(12)erfc(x2), (8) can be written in terms of complementary error function. Pe(γb)=12erfcγb4(1+M2γb)1 Pe=0Pe(γb)fγb(γb)dγb

Substituting the values of fγb(γb) and Pe(γb) from (7), (9) in (10), respectively, the expression for probability of error is given as Pe=14Γ(α)Γ(β)01γberfcγb4(1+M2γb)1×G0,22,0αβγbγb̄|α,βdγb

In order to find analytical expressions for probability of error

Numerical results

In this section, numerical analysis for moderate and strong turbulence conditions taking Gamma–Gamma turbulence model is carried out. Table 2 shows all the values of α and β used for calculation purpose.

Our proposed DCSK-FSO system for Case A is given by (19) and the plot is shown in Fig. 4. The probability of error for moderate and strong turbulence conditions using DCSK modulation and link length L=1000 m is presented in the figure. The value of Cn2 has been taken as 1.75×1013 and 8.04×1014

Conclusion and future scope

The probability of error analysis for DSCK-FSO system is analyzed under different turbulence conditions using numerical approximation techniques. It has been realized that if there is no spreading of the signal at Pe=105 and link length 500 m (refer Fig. 5), the value of SNR is low (35 dB). However, when spreading is considered (M=4) for the same link length at Pe=105 (refer Fig. 8), the value of SNR is reduced to 25 dB. So we can conclude that for same link length, system performance

Ghanishtha Narang received the B.Tech and M.Tech degrees in Electronics and Communication Engineering from Vaish College of Engineering, Rohtak, India and PDM College of Engineering, Bahadurgarh, India in 2013 and 2015, respectively. She is currently working as Research Fellow at THE NORTHCAP UNIVERSITY, Gurgaon, India. Her current study mainly focuses on Optical Wireless Communication and Chaotic Communication.

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    Mona Aggarwal has completed Ph.D. in optical wireless communication from Netaji Subhash Institute of Technology (Delhi University) and currently she is serving as an Assistant Professor in the Electronics and Communication engineering department of THE NORTHCAP UNIVERSITY, Gurgaon, India. Her current research interests are optical wireless communication, visible light communication and power line communication systems.

    Hemani Kaushal received the bachelor’s degree in electronics and communication engineering from Punjab Technical University, India, in 2001, the master’s degree in electronics product design and technology from the PEC University of Technology, Chandigarh, India, in 2003, and the Ph.D. degree in electrical engineering from the Indian Institute of Technology Delhi, India, in 2012. She is currently working with University of North Florida, Jacksonville, USA. She has been in the field of academics for almost 14 years now. She has worked on various industry sponsored projects related to free space optical communication for Indian Space Research Organization, and Aeronautical Development Agency, Department of Defense Research and Development, Bengaluru, India. Her areas of research include wireless communication systems specifically in free-space, underwater, and indoor visible-light optical communications.

    Swaran Ahuja received Ph.D. degree from Indian Institute of Technology, Delhi, India. He is currently working as Professor and Head of the department, EECE, THE NORTHCAPUNIVERSITY, Gurgaon, India. His current work mainly focuses on different aspects of wireless communications with emphasis on channel estimation, diversity techniques, cooperative communication, and free space optics.

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